The Roots and Links in a Class of $M$-Matrices
Xiao-Dong Zhang
TL;DR
This paper investigates the structure of roots and links in a specific class of $M$-matrices related to ultrametric matrices, using the properties of sub-kernel transient matrices and supporting trees.
Contribution
It provides a complete characterization of the roots and links of these $M$-matrices based on their associated supporting trees, advancing understanding of their structure.
Findings
Characterization of exiting roots of sub-kernel transient matrices
Description of links in $M$-matrices via supporting tree structure
Connection between $M$-matrices and generalized ultrametric matrices
Abstract
In this paper, we discuss exiting roots of sub-kernel transient matrices associated with a class of matrices which are related to generalized ultrametric matrices. Then the results are used to describe completely all links of the class of matrices in terms of structure of the supporting tree.
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